Question

Deepak bought a new car at the dealership for $25,000. It is estimated that the value of the car will decrease 9% each year. Which exponential function models the value v of the car after t years?

Answer 1

@Hero @JackJordan

Answer 2

Says "which" meaning, a list of answer choices are available to choose from.

Answer 3

a) v=25,000(1.9)^t
b) (same^^) (0.1)^t
c) (same^^) (0.91)^t
d) (same^^) (1.09)^t

Answer 4

i know its either a or d because the 1 comes before the decimal, but i got confused because i don't remember if the 9 has a 0 infront or not

Answer 5

It's not proper to post answer choices in that manner.

Answer 6

How do you figure that it's either a or d?

Answer 7

Explain how you eliminated b or c.

Answer 8

a) v=25,000(1.9)^t
b) v=25,000(0.1)^t
c) v=25,000(0.91)^t
d) v=25,000(1.09)^t

my b

Answer 9

i remember that the 1 comes before the decimal

Answer 10

1 comes before the decimal for exponential INCREASE.

Answer 11

oh. so when it's not increasing, the 1 comes after the decimal?

Answer 12

? @Hero

Answer 13

Basically, the only the only value of interest for the general formula \(v = 25000^{kt}\) is the k value. If there's an exponential increase, then \(k = 1 + r\) . If there's an exponential decrease, then \(k = 1 - r\) In this case \(r = 0.09\).

Answer 14

so it's (0.91)^t

Answer 15

@Hero

Answer 16

@mathstudent55

Answer 17

The general formula is \(v = 25000k^t\) sorry.

Answer 18

The formula for exponential growth or decay is:

F = P(1 + r)^t

where F = future amount
P = present amount
r = rate of growth or decay
t = number of years
If r is a rate of growth, r is positive.
If r is a rate of decay, r is negative.

You have a rate of decay, so r = -9% = -0.09

\(F = 25,000(1 - 0.9)^t\)

\(F = 25,000(0.91)^t\)

Answer 19

perfect! thank you!

Answer 20

Yw

Answer 21

I wrote the k as an exponent. Sorry about that.